Social anarchism is the dominant historical strand of the anarchist movement. What separates it from the individualist and market-oriented branches is that it rejects private ownership of productive property as well as the state, holding that a free society would coordinate through voluntary association and federation instead of through either markets or central authority.
Mikhail Bakunin gave it its combative early form, and his conflict with Marx inside the First International, ending in his expulsion in 1872, set the permanent terms of the argument between anarchists and Marxists. Bakunin's charge was prophetic in a way his opponents found easy to dismiss at the time: a dictatorship of the proletariat would become a dictatorship over it, because a revolutionary state is still a state and its officials would become a new ruling class. Kropotkin then supplied the constructive theory in The Conquest of Bread (1892) and the naturalistic case in Mutual Aid (1902), arguing against the social Darwinists that cooperation matters at least as much as competition in evolution.
The tradition includes anarcho-communism, collectivist anarchism and anarcho-syndicalism, which located revolutionary agency in the union instead of the party. Its largest practical test came in Spain, where the CNT and allied collectives ran significant parts of Catalonia and Aragon during the civil war of 1936-39, an experiment ended by Franco's victory and, before that, by Stalinist suppression on its own side.
Its core methodological commitment is that means must already embody the ends they aim at, which is why it rejects both capitalist and state-socialist routes to emancipation. The standing objection is that it has no persuasive account of transition or of large-scale coordination under adversarial conditions. Murray Bookchin sharpened that criticism from inside, and his late attack on what he called lifestyle anarchism accused his own movement of retreating from serious institutional thinking.